# What is reactive energy?

If you are interested in saving and energy efficiency, you have surely heard about reactive energy. You have heard that it reduces the efficiency of installations, that it is bad for the power grid, and, above all, that if you consume reactive energy, you have a penalty on your electricity bill. But what exactly is reactive energy?

Explaining the concept of reactive energy is somewhat complicated. If you look it up in a book, they will fill you with complex number equations, phasor algebra, and trigonometric relationships. The problem is that with so much mathematics, there is a risk of forgetting the physical meaning. Because after all, what does it mean for a dipole to absorb complex power?

So, true to the subtitle of this blog, I am going to explain what reactive energy is without using a single equation. Moreover, I am going to show it to you and let you play with it. At the end of this post, you have a complete application to experiment with. But let’s not get ahead of ourselves, and let’s go step by step.

## A review of alternating current

As is well known, the electrical grid we use is actually a source of alternating voltage. In Spain, this alternating voltage has nominal values of 230V between phase and neutral and 50 Hz. This means that the voltage in our plug changes its direction (goes from positive to negative, and back to positive) 50 times every second, and it does work equivalent to that of a continuous voltage source of 230V. In this post, we will take these values, although the results and conclusions are valid for any other value of the grid.

Let’s graph this voltage versus time, measured in electrical degrees (360º electrical degrees will be 1/50Hz = 0.02s),

When we connect an electric charge to alternating voltage, a certain amount of electric current begins to flow through it. Logically, this current is also an alternating function. This means that the electricity changes the direction in which it passes through the charge, from positive to negative and back to positive, 50 times per second.

The electric current that flows is determined solely by the characteristics of the connected load. The amount of electricity, the amplitude of the current wave, is fixed by the impedance of the load. But (and here comes the interesting part for reactive energy) the load also introduces a phase shift between current and voltage. This means that the current wave will advance or delay in time with respect to the voltage wave. This phase shift, which we will measure in electrical degrees, is what generates reactive energy.

But, what causes the voltage and current waves to be out of phase with each other? To explain this, we have to briefly explain the types of loads that exist.

## Types of loads in electricity

In electricity (not to be confused with electronics), there are three types of loads. Resistors, coils, and capacitors. Let’s see the characteristics of each of them.

• Resistors (resistive loads): Any element through which electricity flows offers a certain resistance to being crossed by the current. When crossed by the current, resistances dissipate energy. As an example of large resistances, we can mention the thermal resistances used to generate heat, but it should be noted that any connected load (electric lines, luminaires, motors, etc.) presents a resistance.
• Coils (inductive loads): A coil is formed by an electrical conductor wound on a ferromagnetic core. When a current passes through it, it generates a magnetic field inside it. This magnetic field stores energy and opposes changes in the value of the electric current. Coils are a fundamental part of multiple machines, for example in motors, transformers, and fluorescence equipment.
• Capacitors (capacitive loads): A capacitor is formed by two conductors separated by an insulating material. When current flows through it, it generates an electric field inside it. This electric field stores energy and opposes changes in voltage. Unlike coils, large capacitors have little application in electricity. Their main use is in batteries to compensate, precisely, the reactive effects produced by the coils.

Resistors are passive elements that do not generate a phase shift in the current. However, coils and capacitors are reactive elements that generate, respectively, magnetic and electric fields. These fields present a certain “inertia” to be created or destroyed, and it is this “inertia” that introduces phase shifts in the current. Both elements produce opposite effects on the current, coils introduce negative phase shifts, and capacitors introduce positive ones.

However, real loads are never “pure” but present an intermediate behavior between passive and reactive loads. To characterize real loads, we use the phase angle they introduce between voltage and current. A pure resistor is a load of 0º, a coil 90º, and a capacitor -90º. Mixed behaviors present phase shift values intermediate between these limits.

In the following graph, you can move the bar, modifying the behavior of the load, and observing the phase shift introduced in the electric current.

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## A question of power

Why is this phase shift important and how can it be the cause of reactive energy? To see the effect it has on the load, we will calculate the power consumed by a load, which we obtain by simply multiplying the voltage and the current at each moment in time. The result, S(t), which we will call apparent power, is shown in the following graph.

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It can be observed that the apparent power is a wave with twice the frequency of the voltage. That is, if we connect a lamp (a resistive element, angle 0º), it turns on and off 100 times per second. This fluctuating behavior in power is always fulfilled, for any type of connected load. The effective power value over time is the average of this power, which is shown with the line Smed.

Now, vary the angle of the load and observe how the power wave S(t) starts to take negative values at certain times. Indeed, the load absorbs power during part of the time and gives it back to the grid at another time. Meanwhile, the average power Smed decreases. In the extreme values of 90º or -90º, corresponding to pure inductive or capacitive loads, the value of Smed is zero. In these pure cases, the load absorbs energy for half a period and returns exactly the same energy during the next half period.

It only remains to use a small “mathematical trick” to decompose this apparent power S(t) into the sum of two purely active and reactive components. At all times, the sum of both components is the power S(t), which is the one actually absorbed by the load.

• The real power P(t) is the part of the power that pulses in phase with the voltage. This power, originated by the resistive elements of the load, is the one that actually does useful work.
• The reactive power Q(t) is the power component that pulses at 90 or -90º. It is originated by the reactive elements of the load and does not generate useful work over time.

The amount of each component is marked by the phase shift between voltage and current. Specifically, the relationship between active power and apparent power is the cosine of the angle formed by voltage and current. This relationship is commonly called the power factor of the installation.

The following graph shows the distribution of power between the two components depending on the angle.

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## Conclusion

We have seen that the reactive elements of an electric load introduce phase shifts between voltage and current. This phase shift is caused by the “inertia” of the load in the creation and destruction of magnetic and electric fields. The existence of this phase shift causes the power absorbed by the load, S(t), to take negative values, so the load gives power away for part of the time.

Reactive power is the power component that pulses at 90º with the voltage. The net work it performs over time is zero. The energy absorbed in one half period is stored inside the load in the form of a magnetic or electric field and is entirely released in the next half period. In contrast, active power is the component that pulses at 0º with the voltage and is the one that performs effective work over time.

In a future post, we will see the negative effects of reactive power on an electrical grid, and we will address certain myths and truths related to reactive energy in the field of energy efficiency.

To finish, I leave you with the complete graph with all the magnitudes seen in the post. You can turn on and off the functions you want by clicking on their name in the legend.

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